It's not precisely a "rivalry", but they did, somehow, become competitors, even if it is mostly one-sided.
I think that the relationship between Mello and Near (Death Note) was incredibly interesting, and I really liked that "rivalry", myself. A lot 更多 than l and Light's. They're both just as different from each other as they are similar, and I think that part of what makes it intriguing is that they had such a high potentiality of becoming friends.